To determine the equation of the line of best fit from a graph, follow these steps:

1. **Identify two points on the line of best fit**: Choose two points that lie exactly on the line. For example, let's say the points are (x₁, y₁) and (x₂, y₂).

2. **Calculate the slope (m)**: Use the formula for the slope of a line:
$$
m = \frac{y₂ - y₁}{x₂ - x₁}
$$

3. **Use the slope-intercept form of the equation of a line**: The general form is:
$$
y = mx + b
$$
where $ m $ is the slope and $ b $ is the y-intercept.

4. **Find the y-intercept (b)**: Substitute one of the points (x₁, y₁) and the slope (m) into the equation $ y = mx + b $ and solve for $ b $.

5. **Write the final equation**: Substitute the values of $ m $ and $ b $ into the slope-intercept form.

Let's apply these steps to the given graph:

1. **Identify two points**: Suppose the points on the line of best fit are (2, 5000) and (5, 15000).

2. **Calculate the slope (m)**:
$$
m = \frac{15000 - 5000}{5 - 2} = \frac{10000}{3} \approx 3333.33
$$

3. **Use the slope-intercept form**: Start with $ y = mx + b $.

4. **Find the y-intercept (b)**: Using the point (2, 5000),
$$
5000 = 3333.33 \cdot 2 + b
$$
$$
5000 = 6666.66 + b
$$
$$
b = 5000 - 6666.66
$$
$$
b \approx -1666.66
$$

5. **Write the final equation**:
$$
y \approx 3333.33x - 1666.66
$$

Therefore, the equation of the line of best fit is approximately:
$$
y = 3333.33x - 1666.66
$$

Compare this with the given options (A, B, C) to select the correct one.

Question

To determine the equation of the line of best fit from a graph, follow these steps:

1. **Identify two points on the line of best fit**: Choose two points that lie exactly on the line. For example, let's say the points are (x₁, y₁) and (x₂, y₂).

2. **Calculate the slope (m)**: Use the formula for the slope of a line:
   $$
   m = \frac{y₂ - y₁}{x₂ - x₁}
   $$

3. **Use the slope-intercept form of the equation of a line**: The general form is:
   $$
   y = mx + b
   $$
   where $ m $ is the slope and $ b $ is the y-intercept.

4. **Find the y-intercept (b)**: Substitute one of the points (x₁, y₁) and the slope (m) into the equation $ y = mx + b $ and solve for $ b $.

5. **Write the final equation**: Substitute the values of $ m $ and $ b $ into the slope-intercept form.

Let's apply these steps to the given graph:

1. **Identify two points**: Suppose the points on the line of best fit are (2, 5000) and (5, 15000).

2. **Calculate the slope (m)**:
   $$
   m = \frac{15000 - 5000}{5 - 2} = \frac{10000}{3} \approx 3333.33
   $$

3. **Use the slope-intercept form**: Start with $ y = mx + b $.

4. **Find the y-intercept (b)**: Using the point (2, 5000),
   $$
   5000 = 3333.33 \cdot 2 + b
   $$
   $$
   5000 = 6666.66 + b
   $$
   $$
   b = 5000 - 6666.66
   $$
   $$
   b \approx -1666.66
   $$

5. **Write the final equation**:
   $$
   y \approx 3333.33x - 1666.66
   $$

Therefore, the equation of the line of best fit is approximately:
$$
y = 3333.33x - 1666.66
$$

Compare this with the given options (A, B, C) to select the correct one.

Knowee AI · Accepted Answer